Thanks for the A2A Joel.
Your instincts about what the relationship between oil prices and stock prices "should" logically be is shared by many - in fact a goodly number of market analysts seem to have been anticipating that lower oil prices would have a positive impact on stocks for the reason you point out (i.e. production and transportation costs on the supply side), and because consumers have more disposable income when oil prices remain low. Except...well, it hasn't played out that way.
Why? Frankly I don't think anyone really knows. Some of the opinions in other answers here are interesting, but they are primarily speculation. One theory that hasn't been discussed is that the correlation between oil and stocks is a result of investor risk aversion: investors are seeking safe havens in uncertain times, and both oil and stocks are perceived as volatile right now. At least this is one way to explain the correlation. Another is that "oil is driving sentiment;" that is, acute awareness of oil price fluctuations is having a psychological impact on the market. Again, though, nobody is sure why this is happening, as oil volatility doesn't correlate precisely with economic productivity or other predictive metrics.
Here is how one CNN Money article describes the psychological correlation (i.e. what investors are thinking low oil prices mean...even if they don't really mean those things):
"-- Falling prices often signal softness in demand that can foretell an economic slowdown. However, many experts believe this oil crash is mostly being caused by the epic supply glut, not weak demand.
-- Cheap oil is causing U.S. oil production to cool off, weighing on profits from energy companies and the economies of states like Texas and North Dakota.
-- The threat of billions of dollars of oil loans imploding raises the risk of trouble in the banking sector.
-- Chaos in the oil patch is causing junk bond yields to spike, especially in the energy sector.
-- Russia, Venezuela, Brazil and other countries that rely on oil exports are slumping badly, causing concern about a new emerging market debt crisis.
-- Falling energy prices and the global stock market reaction have cast fresh doubt on whether the Federal Reserve will be able to raise interest rates this year."
Still other folks speculate that the correlation is a predictable consequence of fluctuations in aggregate demand...but that doesn't fully explain things either.
As with many issues in our complexly interdependent modernity, no one really understands how the global economy functions - at least not in a way that can anticipate and explain correlations like this one. There are plenty of theories and grand generalizations, but even in hindsight it's extremely difficult to tease out all of the causal links - especially since many critical events are the result of undisclosed backroom deals, deceptive business practices, cronyiest manipulations, and unanticipated externalities.
My 2 cents.
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